{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Interface-fitted Mesh Generator: Two Dimensions\n",
    "\n",
    "We explain a simple mesh generator for generating an interface-fitted mesh in two dimensions. \n",
    "\n",
    "**Algorithm:  2D Interface-fitted Mesh Generation**\n",
    "\n",
    "0. Generate a uniform Cartesian mesh of the box\n",
    "\n",
    "1. Find points near the interface. \n",
    "    - cut points\n",
    "    - mesh points near or on the interface\n",
    "    - centers of special elements.\n",
    "\n",
    "2. Construct a Delaunay triangulation on these points.\n",
    "\n",
    "3. Post processing. \n",
    "    - remove triangles away from the interface\n",
    "    - merge all uncut elements\n",
    "    \n",
    "    \n",
    "**Reference**: L. Chen, H. Wei, M. Wen. [An Interface-Fitted Mesh Generator and Virtual Element Methods for Elliptic Interface Problems](https://www.math.uci.edu/~chenlong/interface_vem.html). *Journal of Computational Physics*. 334(1), 2017, 327–348."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generate a uniform Cartesian mesh of the box"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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UUgvRH62u9sf/gnfZT2fBkcgSz/L/GzbD7xTrGl22NuL9qMRzLvHQuv1hxI3S5lyyHs42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\noWIDegAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "box = [ -1, 1, -1, 1];\n",
    "h = 0.1;\n",
    "[node,elem,T] = squarequadmesh(box,h);\n",
    "edge = T.edge;\n",
    "edge2elem = T.edge2elem;\n",
    "clear T;\n",
    "N = size(node,1);\n",
    "NT = size(elem,1);\n",
    "showmesh(node,elem);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Find points near the interface"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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R2hERV3xf3N5/iuy5k+ZbpDpuOaeVZxr0mYaCBC2hZW9Gar1729r8+GZ+0IPz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\nIAEAjEBBAgAYgYIEADACBQkAYIT/DzqdUwn1oKnVAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "phi = @phiheart;\n",
    "showmesh(node,elem);\n",
    "hold on;\n",
    "\n",
    "% compute the phi value at each vertex\n",
    "phiValue = phi(node);\n",
    "phiValue(abs(phiValue) < eps*h) = 0;  % treat nearby nodes as on the interface\n",
    "vSign = sign(phiValue);\n",
    "findnode(node,vSign==0);\n",
    "\n",
    "% Find the intersection points between edges and the interface\n",
    "isCutEdge = (vSign(edge(:,1)).* vSign(edge(:,2))<0);\n",
    "findedge(node,edge,isCutEdge,'noindex','draw');\n",
    "A = node(edge(isCutEdge,1),:);\n",
    "B = node(edge(isCutEdge,2),:);\n",
    "cutNode = findintersectbisect(phi,A,B);\n",
    "Ncut = size(cutNode, 1);\n",
    "vSign(N+1:N+Ncut) = 0;\n",
    "findnode(cutNode,'all','noindex','color','b','MarkerSize',12);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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VwSOkVWgaXt/++Nnb+tnh6jLQBC6vs8pSGWjQKPlcBlpTOwPNtGntr7qmJY8u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\nok/X/X3RAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "showmesh(node,elem);\n",
    "hold on;\n",
    "% find interface elem and nodes\n",
    "isInterfaceElem = false(NT,1);  \n",
    "isInterfaceElem(edge2elem(isCutEdge,[1,2])) = true;\n",
    "isInterfaceElem(sum(abs(vSign(elem)), 2) < 3) = true; % 2 vertices on interface\n",
    "findelem(node,elem,isInterfaceElem,'noindex');        \n",
    "\n",
    "isInterfaceNode = false(N,1);\n",
    "isInterfaceNode(elem(isInterfaceElem,:)) = true;\n",
    "findnode(node,isInterfaceNode,'noindex','MarkerSize',12);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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UUgvRH62u9sf/gnfZT2fBkcgSz/L/GzbD7xTrGl22NuL9qMRzLvHQuv1hxI3S5lyyHs42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\noWIDegAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "showmesh(node,elem);\n",
    "hold on;\n",
    "% add centers of special elements (two vertices on the interface)\n",
    "%  0 - -1    -1 - 0     0 -  0      1 - 0\n",
    "%  1 -  0     0 - 1     1 - -1      1 - 0\n",
    "isSpecialElem = (sum(abs(vSign(elem)),2) <= 2); % two or more vertices on interfaces\n",
    "% isSpecialElem = (sum(vSign(elem),2) == 0) & (sum(abs(vSign(elem)),2) == 2);\n",
    "specialElem = elem(isSpecialElem,:);\n",
    "auxPoint = (node(specialElem(:,1),:) + node(specialElem(:, 3),:))/2.0;\n",
    "Naux = size(auxPoint,1);\n",
    "vSign(N+Ncut+1:N+Ncut+Naux) = sign(phi(auxPoint));\n",
    "% find the first two cases\n",
    "isDiagInterface = (vSign(specialElem(:,1)).*vSign(specialElem(:,3)) == -1) | ...\n",
    "                  (vSign(specialElem(:,2)).*vSign(specialElem(:,4)) == -1);\n",
    "vSign(N+Ncut+find(isDiagInterface)) = 0;            \n",
    "findnode(auxPoint,'all','noindex','color','m');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Vbdsf6nl+Xwg5rgqpYbBoIFWSzHNxQJbkuahGnr/Tc38ObQacslsH3dpPFHugvU9dq1jY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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "% add cut points and aux points\n",
    "node = [node; cutNode; auxPoint];\n",
    "nearInterfaceNode = [node(isInterfaceNode,:); cutNode; auxPoint];\n",
    "interfaceNodeIdx = [find(isInterfaceNode); N+(1:Ncut)'; N+Ncut+(1:Naux)'];\n",
    "showmesh(node,elem);\n",
    "findnode(nearInterfaceNode,'all','noindex','color','r','MarkerSize',11);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Construct a Delaunay triangulation on these points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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5NKWRJSmBRt7MfU8TZvJfbGx13ELNhK7g7Wyn9BDfXwtyaDtRWX1Zt7rfcabg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QhLuJ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\nQmCC\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "% construct the Delaunay triangulation of interfaceNode\n",
    "% different versions of matlab using different delaunay triangulation\n",
    "matlabversion = version();\n",
    "if str2double(matlabversion(end-5:end-2)) <= 2013\n",
    "    DT = DelaunayTri(nearInterfaceNode); %#ok<*DDELTRI>\n",
    "    tElem = DT.Triangulation;\n",
    "else\n",
    "    DT = delaunayTriangulation(nearInterfaceNode);\n",
    "    tElem = DT.ConnectivityList;\n",
    "end\n",
    "tElem = fixorder(nearInterfaceNode,tElem); % correct the orientation\n",
    "showmesh(node,tElem);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Delaunay triangulation is a mesh for the coonvex hull of the given points. Without postprocess, it is messy. \n",
    "\n",
    "## Post-processing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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t7vPddd+J0FQi5GMMXP7iveRL9vUfgIL0LGqdqPfMT3rpUzdIHIyZT7MwxhhW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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "% get rid of the unnecessary triangles\n",
    "NI = sum(isInterfaceNode);  % number of pts of the background mesh near interface\n",
    "haveNewPts = (sum(tElem > NI,2) > 0); % triangles containing new added vertices\n",
    "tElem = tElem(haveNewPts,:); \n",
    "tElem = interfaceNodeIdx(tElem);  % map interfaceNode index to node index\n",
    "showmesh(node,tElem,'Facecolor','y');\n",
    "findnode(node,vSign==0,'noindex');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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rDW1EGzXERr4PpYCL5EfTLQ8ohDaqHgqpTiq2UdofYThM1jE8q2amNtBGtFET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\nQqoC2og2oo1oI7ITtp+ogjIf+I9fvat3Th94fT1z/cCbu0f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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "% get the remainding quad elems\n",
    "sElem = elem(~isInterfaceElem,:);\n",
    "% merge into one triangulation\n",
    "elem = [tElem; sElem(:,[2 3 1]); sElem(:,[4 1 3])];\n",
    "T = auxstructure(tElem);\n",
    "showmesh(node,elem); hold on;\n",
    "showmesh(node,tElem,'Facecolor','y');\n",
    "isInterfaceEdge = ((vSign(T.edge(:,1)) == 0) & vSign(T.edge(:,2)) == 0);\n",
    "interfaceEdge = T.edge(isInterfaceEdge,:);\n",
    "nearInterfaceNode = find(vSign == 0);\n",
    "findedge(node,interfaceEdge,'all','noindex','draw');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "%% Generate interface data\n",
    "interface.vSign = vSign;\n",
    "interface.tElem = tElem;\n",
    "interface.sElem = sElem;\n",
    "interface.edge = interfaceEdge;\n",
    "interface.node = nearInterfaceNode;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Further Reading\n",
    "\n",
    "Run the following example in MATLAB and read `interfacemeshdoc` to learn more."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "box = [ -1, 1, -1, 1];\n",
    "[node,elem,interface] = interfacemeshdoc(box,@phiheart,0.05);\n",
    "showmesh(node,elem);\n",
    "findedge(node,interface.edge,'all','noindex','draw');"
   ]
  }
 ],
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   "file_extension": ".m",
   "help_links": [
    {
     "text": "MetaKernel Magics",
     "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
    }
   ],
   "mimetype": "text/x-matlab",
   "name": "matlab",
   "version": "0.14.3"
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  "toc": {
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   "moveMenuLeft": true,
   "nav_menu": {
    "height": "30px",
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   "navigate_menu": true,
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   "toc_section_display": "block",
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